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Simplifying R(x) = -25x2 + 250x Multiply R * x xR = -25x2 + 250x Reorder the terms: xR = 250x + -25x2 Solving xR = 250x + -25x2 Solving for variable 'x'. Reorder the terms: -250x + xR + 25x2 = 250x + -25x2 + -250x + 25x2 Reorder the terms: -250x + xR + 25x2 = 250x + -250x + -25x2 + 25x2 Combine like terms: 250x + -250x = 0 -250x + xR + 25x2 = 0 + -25x2 + 25x2 -250x + xR + 25x2 = -25x2 + 25x2 Combine like terms: -25x2 + 25x2 = 0 -250x + xR + 25x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-250 + R + 25x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-250 + R + 25x)' equal to zero and attempt to solve: Simplifying -250 + R + 25x = 0 Solving -250 + R + 25x = 0 Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + R + 250 + 25x = 0 + 250 Reorder the terms: -250 + 250 + R + 25x = 0 + 250 Combine like terms: -250 + 250 = 0 0 + R + 25x = 0 + 250 R + 25x = 0 + 250 Combine like terms: 0 + 250 = 250 R + 25x = 250 Add '-1R' to each side of the equation. R + -1R + 25x = 250 + -1R Combine like terms: R + -1R = 0 0 + 25x = 250 + -1R 25x = 250 + -1R Divide each side by '25'. x = 10 + -0.04R Simplifying x = 10 + -0.04RSolution
x = {0, 10 + -0.04R}
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